On Krause's Multi-Agent Consensus Model With State-Dependent Connectivity

By Vincent D. Blondel, Julien M. Hendrickx, John N. Tsitsiklis. IEEE Transactions on Automatic Control, 2008

464 citations recorded by the source corpus.

We study a model of opinion dynamics introduced by Krause: each agent has an opinion represented by a real number, and updates its opinion by averaging all agent opinions that differ from its own by less than one. We give a new proof of convergence into clusters of agents, with all agents in the same cluster holding the same opinion. We then introduce a particular notion of equilibrium stability and provide lower bounds on the inter-cluster distances at a stable equilibrium. To better understand the behavior of the system when the number of agents is large, we also introduce and study a variant involving a continuum of agents, obtaining partial convergence results and lower bounds on inter-cluster distances, under some mild assumptions.

Subfields: Atomic and Molecular Physics, and Optics, Management Science and Operations Research, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/70129f6da3c7949b18e68776bfabfac782686bea

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In Atomic and Molecular Physics, and Optics

Francesco Bullo

In Management Science and Operations Research

In Statistical and Nonlinear Physics

Citations in the corpus

Novel Multidimensional Models of Opinion Dynamics in Social Networks (2015, background): “This principle is prominently manifested by various bounded confidence models, where the agents completely ignore the opinions outside their confidence intervals [2]–[5].”
Opinion Dynamics and Learning in Social Networks (2011, background): “The convergence of beliefs in these models is studied in [68], which under mild conditions on the weight matrix T (x(k)), shows that the set of agents can be partitioned into groups such that each group reaches a consensus (see also [17] for a proof of convergence on Krause’s model and properties of”
Opinion Dynamics and the Evolution of Social Power in Influence Networks (2015, background): “In bounded-confidence models, each individual interacts with only those individuals whose opinions are close enough to its own: synchronous [40, 52, 11, 58] as well as pairwise asynchronous [22, 74] updates have been studied.”
Continuous and discontinuous opinion dynamics with bounded confidence (2012, background): “Starting from these works, others have contributed in recent years to this line of research [15, 2].”